The Fortress Language Specification - CiteSeerX

Here we present only the trait Q and its methods. The other rational types have exactly the same methods and differ
only in the details of the types of method arguments and results and exactly what traits are extended by each rational
type. For example, Q is a field and is totally ordered, Q ∗ is totally ordered but is not a field, and Q # is neither
totally ordered nor a field. For the exact details of how all this is implemented, see Section 38.1.
trait Q
extends { R, Q ∗ ,
FieldQ, Q≠, +, −, ·, /,
FieldQ, Q≠, +, −, ×, /,
FieldQ, Q≠, +, −,juxtaposition, /,
TotalOrderOperatorsQ, ,CMP }
coercion ( : Identity+) = 0
coercion ( : Identity·) = 1
coercion ( : Identity×) = 1
coercion ( : Identityjuxtaposition) = 1
coercion ( : Zero·) = 0
coercion ( : Zero×) = 0
coercion ( : Zerojuxtaposition) = 0
opr juxtaposition (self,other: Q): Q
opr +(self): Q
opr +(self,other: Q): Q
opr −(self): Q
opr −(self,other: Q): Q
opr ·(self,other: Q): Q
opr ×(self,other: Q): Q
opr /(self): Q ∗
opr /(self,other: Q): Q #
opr _(self,power: Z): Q #
opr (self,other: Q): Boolean
opr CMP(self,other: Q ∗ ):TotalComparison
opr CMP(self,other: Q # ):Comparison
opr MAX(self,other: Q): Q
opr MIN(self,other: Q): Q
opr MAXNUM(self,other: Q): Q
opr MINNUM(self,other: Q): Q
opr |self| : Q ≥
signum(self): Z
numerator(self): Z
denominator(self): Z
floor(self): Z
opr ⌊self⌋: Z
ceiling(self): Z
opr ⌈self⌉: Z
round(self): Z
truncate(self): Z
opr ⌊self ⌋: N
opr ⌈self ⌉: N
opr ⌊self ⌋: N
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